Quantum entanglement and nonlocality properties of two-mode Gaussian squeezed states

Quantum entanglement and nonlocality properties of a family of two-mode Gaussian pure states have been investigated. The results show that the entanglement of these states is determined by both the two-mode squeezing parameter and the difference of the two single-mode squeezing parameters. For the same two-mode squeezing parameter, these states show larger entanglement than the usual two-mode squeezed vacuum state. The violation of Bell inequality depends strongly on all the squeezing parameters of these states and disappears completely in the limit of large squeezing. In particular, these states can exhibit much stronger violation of local realism than two-mode squeezed vacuum state in the range of experimentally available squeezing values.     

Quantum entanglement and quantum nonlocality for N-photon entangled states

Quantum entanglement and quantum nonlocality of N-photon entangled states |\psi_{N m}\rangle =C_m[\cos\gamma|N-m\rangle₁|m\rangle₂ +\e^{\i\θ_m}\sin\gamma|m\rangle₁|N-m\rangle₂] and their superpositions are studied. We point out that the relative phase θ_m affects the quantum nonlocality but not the quantum entanglement for the state |\psi_{N m}\rangle. We show that quantum nonlocality can be controlled and manipulated by adjusting the state parameters of |\psi_{N m}\rangle, superposition coefficients, and the azimuthal angles of the Bell operator. We also show that the violation of the Bell inequality can reach its maximal value under certain conditions. It is found that quantum superpositions based on |\psi_{N m}\rangle can increase the amount of entanglement, and give more ways to reach the maximal violation of the Bell inequality.     

Relativity and lorentz invariance of entanglement distillability

We study entanglement distillability of bipartite mixed spin states under Wigner rotations induced by Lorentz transformations. We define weak and strong criteria for relativistic isoentangled and isodistillable states to characterize relative and invariant behavior of entanglement and distillability. We exemplify these criteria in the context of Werner states, where fully analytical methods can be achieved and all relevant cases presented.     

Quantum nonlocality

It is argued that the validity of the predictions of quantum theory in certain spincorrelation experiments entails a violation of Einstein's locality idea that no causal influence can act outside the forward light cone. First, two preliminary arguments suggesting such a violation are reviewed. They both depend, in intermediate stages, on the idea that the results of certain unperformed experiments are physically determinate. The second argument is entangled also with the problem of the meaning of physical reality. A new argument having neither of these characteristics is constructed. It is based strictly on the orthodox ideas of Bohr and Heisenberg, and has no realistic elements, or other ingredients, that are alien to orthodox quantum thinking.This work was supported by the Director, Office of Energy Research, Office of High Energy and Nuclear Physics, Division of High Energy Physics of the U.S. Department of Energy under Contract DE-AC03-76SF00098.     

Randomness versus nonlocality and entanglement

The outcomes obtained in Bell tests involving two-outcome measurements on two subsystems can, in principle, generate up to 2?bits of randomness. However, the maximal violation of the Clauser-Horne-Shimony-Holt inequality guarantees the generation of only 1.23?bits of randomness. We prove here that quantum correlations with arbitrarily little nonlocality and states with arbitrarily little entanglement can be used to certify that close to the maximum of 2?bits of randomness are produced. Our results show that nonlocality, entanglement, and randomness are inequivalent quantities. They also imply that device-independent quantum key distribution with an optimal key generation rate is possible by using almost-local correlations and that device-independent randomness generation with an optimal rate is possible with almost-local correlations and with almost-unentangled states.     

Small accessible quantum information does not imply security

The security of quantum key distribution is typically defined in terms of the mutual information between the distributed key S and the outcome of an optimal measurement applied to the adversary's system. We show that even if this so-called accessible information is small, the key S might not be secure enough to be used in applications such as one-time pad encryption. This flaw is due to a locking property of the accessible information: one additional (physical) bit of information can increase the accessible information by more than one bit.     

Quantum nonlocality in weak-thermal-light interferometry

In astronomy, interferometry of light collected by separate telescopes is often performed by physically bringing the optical paths together in the form of Young's double-slit experiment. Optical loss severely limits the efficiency of this so-called direct detection method, motivating the fundamental question of whether one can achieve a comparable performance using separate optical measurements at the two telescopes before combining the measurement results. Using quantum mechanics and estimation theory, here I show that any such spatially local measurement scheme, such as heterodyne detection, is fundamentally inferior to coherently nonlocal measurements, such as direct detection, for estimating the mutual coherence of bipartite thermal light when the average photon flux is low. This surprising result reveals an overlooked signature of quantum nonlocality in a classic optics experiment.     

Local indistinguishability: more nonlocality with less entanglement

We provide a first operational method for checking local indistinguishability of orthogonal states. It originates from that in Ghosh et al. [Phys. Rev. Lett. 87, 5807 (2001)]], though we deal with pure states. Our method shows that probabilistic local distinguishing is possible for a complete multipartite orthogonal basis if and only if all vectors are product. Also, it leads to local indistinguishability of a set of orthogonal pure states of 3 multiply sign in circle 3, which shows that one can have more nonlocality with less entanglement, where "more nonlocality" is in the sense of "increased local indistinguishability of orthogonal states." This is, to our knowledge, the only known example where d orthogonal states in d multiply sign in circle d are locally indistinguishable.     

Quantum nonlocality as an axiom

In the conventional approach to quantum mechanics, indeterminism is an axiom and nonlocality is a theorem. We consider inverting the logical order, making nonlocality an axiom and indeterminism a theorem. Nonlocal superquantum correlations, preserving relativistic causality, can violate the CHSH inequality more strongly than any quantum correlations.     

Output nonlocality and nonclassicality in a two-mode entanglement laser

Output nonlocality and nonclassicality for the two modes are investigated in an entanglement laser sys-tem. Within the framework of a quantum theory of multiwave mixing,nonlocality and nonclassicality are discussed according to the violations of Bell inequality and Cauchy-Schwarz inequality. It is found that both nonlocality and nonclassicality can be fulfilled in the outside cavity fields under certain conditions. It is also shown that there are some nonclassical states that do not show nonlocality.     

Quantum nonlocality without counterfactual definiteness?

Stapp's recent proof of the nonlocality of quantum mechanics is critically discussed. It is demonstrated that in his derivation of the Bell inequalities an extra requirement, over locality, is used, which is tantamount to counterfactual definiteness, and that is not a consequence of locality.1. Research associate N.F.W.O. (Belgium).     

How the Hawking effect and prepared states affect entanglement distillability of Dirac fields

How the Hawking effect and the prepared states influence the entanglement distillability of Dirac fields in the Schwarzschild spacetime is studied by using the Werner states which are composed of the maximum or generic entangled states. It is found that the states are entangled when the parameter of the Werner states, F  , satisfies τ<F?1$\tau <F?1$ in which τ is influenced both by the Hawking temperature of the black hole and energy of the fields. It is also shown that although the parameter of the generic entangled states, α, affects the entanglement, it does not change the range of the parameter, F, where the states are entangled for the case of generic entangled states.     

Steering, entanglement, nonlocality, and the Einstein-Podolsky-Rosen paradox

The concept of steering was introduced by Schr?dinger in 1935 as a generalization of the Einstein-Podolsky-Rosen paradox for arbitrary pure bipartite entangled states and arbitrary measurements by one party. Until now, it has never been rigorously defined, so it has not been known (for example) what mixed states are steerable (that is, can be used to exhibit steering). We provide an operational definition, from which we prove (by considering Werner states and isotropic states) that steerable states are a strict subset of the entangled states, and a strict superset of the states that can exhibit Bell nonlocality. For arbitrary bipartite Gaussian states we derive a linear matrix inequality that decides the question of steerability via Gaussian measurements, and we relate this to the original Einstein-Podolsky-Rosen paradox.     

Quantum nonlocality and interference in frequency domain

The experiment is proposed which should demonstrate that if the filter providing the spectral selection is placed in the route of one photon of the entangled pair produced by spontaneous down-conversion and the photon is detected behind it then the interference appears in the (distant) Mach-Zehnder interferometer placed in the route of the other photon of the pair even if the optical path difference through the interferometer greatly exceeds the coherence length of the light and if the spectra of these two photons do not overlap. The theoretical analysis is carried out and physical interpretation is discussed.     

Quantum interference and entanglement of photons that do not overlap in time

We discuss the possibility of quantum interferences and entanglement of photons that exist at different intervals of time, i.e., one photon being recorded before the other has been created. The corresponding two-photon correlation function is shown to violate Bell's inequalities.     

Quantum nonlocality and partial transposition for continuous-variable systems

A continuous-variable Bell inequality, valid for an arbitrary number of observers measuring observables with an arbitrary number of outcomes, was recently introduced [Cavalcanti, Phys. Rev. Lett. 99, 210405 (2007)10.1103/PhysRevLett.99.210405]. We prove that any n-mode quantum state violating this inequality with quadrature measurements necessarily has a negative partial transposition. Our results thus establish the first link between nonlocality and bound entanglement for continuous-variable systems.     

Quantum nonlocality can be distributed via separable states

正Quantum nonlocality is one of the most astonishing features in quantum physics.It is of great importance in understanding the conceptual foundations of quantum theory and is closely related to certain quantum information processing such as quantum protocols for decreasing communication complexity[1]and secure quantum communication[2,3],see refs.[4-9]for more details.     

Quantum transfer functions,weak nonlocality and relativity

The method of transfer functions is developed as a tool for studying Bell inequalities, alternative quantum theories and the associated physical properties of quantum systems. Non-negative probabilities for transfer functions result in Bell-type inequalities. The method is used to show that all realistic Lorentz-invariant quantum theories, which give unique results and have no preferred frame, can be ruled out on the grounds that they lead to weak backward causality.     

Quantum theory does not require action at a distance

The question of whether or not the correlations predicted by quantum theory and actually observed in EPR-type experiments can be understood without assuming action at a distance is still controversial. The author's point of view, expressed by the title of this paper, is substantiated by the discussion of a specific example, and is defended against some recent criticism by H. P. Stapp.1. These predictions arenot exhausted by Eq. (1); see [9].